[FEATURE] VSCode extension: restore ability to delete a session

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

I want to be able to delete (local) sessions when using the VSCode extension.
This was previously possible, but was intentionally changed in 2.1.257.

Proposed Solution

Restore the deletion functionality.

If accidental deletion is a concern, add a confirmation prompt.

Alternative Solutions

I'm currently deleting sessions manually from disk but that is not convenient.

Priority

Medium - Would be very helpful

Feature Category

Developer tools/SDK

Use Case Example

Example scenario:

1. I prompt Claude Code VSCode extension with a question
2. I get the answer that I was looking for
3. I want to delete the session

Additional Context

_No response_